Rolf,
you cannot put a 'normal' bullet like the Barnes 36gn into the Long Rifle case, as it will expand the case-mouth drastically and won't chamber.
The reason is that the Short, Long, and Long Rifle still use the now archaic 'heeled' bullet form. The bullet body is the full barrel groove diameter of a shade over 0.223", but the bit that slots into the case is a smaller diameter stub or 'heel'. If you look at a .22LR round, you'll see that the OD of the case is virtually identical to that of the bearing area on the bullet body, only marginally larger at a nominal 0.224".
So, stick a 0.224" jacketed bullet into a .22LR case and as there is no 'heel', the case body will be expanded by several thou' as the bullet is seated making it substantially oversize for the .22LR chamber, probably ending up same as the .22 Magnum at 0.240".
Then there is the issue of powder type / charge - standard velocity .22LR uses tiny charges of very fast burning propellants specially suited to a bullet whose material is alloyed to be only slightly harder than pure lead, and charge weighst are usually only 1.5-2.0gn. Throw in an oversize and much harder jacketed bullet and even if the round would chamber who knows what sort of pressures you'd get.
.22WMR (magnum) uses the 'normal' set-up of a full-size (0.224") jacketed bullet with part of its full-diameter section seated inside the case and the OD is therefore bullet dia + 2 x case wall thickness, which according to COTW is 0.240".
You could therefore in theory pull the factory bullet from a .22WMR cartridge and replace it with one of your choice in a similar weight. Apart from the usual caveats about same weight bullets not always producing same pressures in such substitutions, there is the (not so) slight problem of 'pulling' the factory bullet. It's unlikely a collet puller would find enough full-dia bullet body for a good grip, and one is always advised NEVER to use rimfire cartridges in hammer-type inertia pullers as there is a risk of compressing the rim enough to cause ignition. With light bullets and a heavy case-mouth crimp the norm, you'd have real trouble getting the bullet out in any event.
The answer to improving the .22LR with HV jacketed bullets is called either .17HMR, .17 Mach2, or .22WMR, and Hornady / Winchester got there a while back.
Laurie,
York, England